On a set S, we say that $\leq$ is a partial ordering, if for $s_1,s_2,s_3 \in S$
1. $s_1\leq s_2, s_2 \leq s_1 \Longrightarrow s_1=s_2$
2. $s_1 \leq s_2 \leq s_3 \Longrightarrow s_1 \leq s_3$
3. $s_1 \leq s_1$